Pick a name that concisely describes what's in the data sheet. E.g., I think "A7108" is a good name for the A7108* data sheet. If a data sheet describes a small number of different parts, you can use aliases to name them. dsv is meant as an interactive tool for humans, so the name should be something that's easy to remember and convenient to type. Also, names in dsv can be project-specific. There's no need for them to be globally unique. The names or what they refer to can also change over time.

The name of a component should include enough information that one can pick a functionally compatible part without having to consult other resources. E.g., A7108 is insufficient, because you don't know the voltage or whether it's the -ADJ variant.

If the part comes in different packages but with otherwise identical electrical properties, I would not consider it important to include the package. (We have the - normally invisible - footprint field for that.)

For some parts, there may be electrical or other properties we depend on - e.g., maximum power dissipation - that change with the package. In this case, there should be some guidance in the schematics, e.g., a more complete component name, the footprint, or the parameter(s) in question. In some cases, one may not know the naming scheme well enough to be able to tell which name is "sufficient". In this case, I'd just err on the side of being overly specific.